_Australia �Finlonl Irelonl Sources: World Investment Report (various issues).
6.5 MODEL SPECIFICATION AND ESTIMATION P ROCED URE
The theoretical arguments discussed in Section 6.2 indicated the variables that have been tested to identify the impact of FDI on the economy are interrelated, thus suggesting the models need to be analysed within a systems approach, in addition to the established single equation approach. In time-series modelling, as an alternative to single equation modelling, VAR models have now become an integral part of econometrics. The VAR methodology developed by Sims (1 980) helps meet the need for a multivariate model that could estimate relationships among jointly endogenous variables without placing a priori restrictions on them. In this V AR methodology each variable will be regressed on its own lagged values as well as those of other explanatory variables in the equation. Pesaran and Pesaran ( 1 997) provide a detailed econometric explanation of the VAR methodology that has been used in this study.
After the identification of the stationarity properties of the variables that have been included in the models, this study defmes the vector of potentially endogenous variables to be Zt, as an unrestricted VAR in the following manner:
p
Z, = ao + L tP;Z,_; + If/w, + J.l, (6.2)
;=1
where, Zt is a (m x l) vector of jointly determined dependent v ariables (i.e., all the variables that have been included in the equations); ao is a (m x 1) column vector; tP; is
a (m x m) matrix of coefficients to be estimated; Wt is a (q x 1) vector of deterministic or exogenous variables; and J.l, is a (m x l) vector of unobsevered disturbances assumed to satisfy the following assumptions:
• Zero mean assumption: The (m x 1) vector of disturbances, J.l/, has zero mean:
E(J.lJ = 0 for t = 1 , 2, . .. , n
• Homoskedasticity assumption: The (m x l) vector of disturbances, J.l/, has a time invariant conditional variance matrix;
• Non-autocorrelated error assumption: The (m x l) vector of disturbances, J.l/, is serially uncorrelated;
• Orthogonality assumption: The (m x l) vector of disturbances, J.l/, and the regressors w are uncorrelated;
• Stability assumption: The augmented VAR (P) is stable, i.e. all the roots of the following determinantal equation fall outside the unit circle;
• Normality assumption: The (m x l) vector of disturbances, J.l/, has a multivariate
normal distribution.
The single equation models developed in Chapter Four have been employed to test the significance of the variables and the impact of FDI on suggested key macroeconomic variables. The results are reported and discussed in Chapter Five. Based on those results
(i.e. t he finally estimated e quations a re s elected a s the s uperlative models t o t est t he hypothesis set out in Chapter One) the parsimonious models have been selected as the
robust equation for the VAR system to be built up in this Chapter. As shown below, in
the V AR system all variables8 are considered endogenously.
The growth model, based on the [mally estimated growth equation (S. lb), is given as (6.3) in the VAR model as follows:
GDp, GDp'_1 GDP'_n
Kt,t Kt,t-I Kt,t-n
Kpri,t Kpri,t_1 Kpri,t-n
KpUb,t
= Ao + AI
Kpub,t-I + .... + An Kpub,t-n+
If/CERt+
f-Lt (6.3)Xt Xt_1 Xt_n
Lt Lt_1 Lt_n
GDPPCt GDPPCt_1 GDPPCt_n
HCt HCt_1 HCt_n
1.1. = error terms for the variables included; Al -An = are 8 x 8 matrices of coefficients;
Ao = 8 x 1 vector of intercepts; CERt = 8 x 1 vector of elements representing the Close
Economic Relations (CER) dwruny variable; and If = 8 x 8 matrix of coefficients of
the CER dummy variable.
B ased on the empirical e vidence found in Chapter F ive the I mports Model with F DI flow, i.e. equation (S.2b) is represented by (6.4) as follows:
I Mt IMt-l IMt_n
FDlt FDlt-l FDlt_n
Ipri,t
= Ao
+ AI Ipri,t-I+
.... + An I pri,r-n + f-Lr (6.4)REXr REXr_1 REXr_n
GDPPCt GDPPCr_1 GDPPCt_n
S All variables are expressed in logs and full description of the variables is given in Table 4 . 1
J.l. = error terms for the variables included; AI -.\ = are 5 x 5 matrices of
coefficients; Ao = 5 x 1 vector of intercepts.
FDI stock equation (5.3a) is shown as (6.5):
I Mt IMt_1 IMt_n
Kt,t Kt,t-' Kt,t-n
Kpri,t =
Ao
+ A, Kpri,t-I + .... + .\ Kpri,t-nREXt REXt_, REXt_n
GDPPCt GDPPCt_, GDPPCt_n
J.l. = error terms for the variables included; AI -An
coefficients; Ao = 5 x 1 vector of intercepts.
+ Pt (6.5)
are 5 x 5 matrices of
In a s imilar v ein, b asing t he finally estimated s ingle e quation for Exports M odel t he
V AR equations for FDI flow and stock are given as equation (6.6) and (6.7) below:
FDI Flow equation (5.4b) is represented as (6.6):
Xt Xt_1 Xt_n
FDI, FDI,_, FDIt_n
Ipri,t = Ao + � Ipri,t_1 + .... + An Ipri,t-n + If/CERt + Pt (6.6)
REXt REXt_, REXt_n
Lt Lt_I Lt-n
J.l. = error terms for the variables included; AI -An = are 5 x 5 matrices of coefficients; Ao =; 5 x 1 vector of intercepts; CERt = 5 x 1 vector of elements
representing the Close Economic Relations (CER) dummy variable; and If = 5 x 5
The corresponding FDI stock equation (5.5) is represented as (6.7):
Xt Xt_1 Xt-n
Kf,t Kf,t-I Kf,t-n
Kpri,t = Ao + � Kpri,t-I + .... + An Kpri,t-n + IjICERt + Pt (6.7)
Kpub,t Kpub,t-I Kpub,t-n
REXt REXt_1 REXt_n
Lt Lt_I Lt_n
Jl = error tenus for the variables included; Al -An = are 6 x 6 matrices of
coefficients; Ao = 6 x 1 vector of intercepts; CERt = 6 x 1 vector of elements
representing t he C loser Economic R elations ( CER) dummy v ariable; a nd IjI = 6 x 6
matrix of coefficients of CER dummy variable.
Based on the fmal estimation models of single equation the capital formation models are specified in the following manner.
Total domestic investment equation (5.6) is specified as (6.8): TDlt FDlt DCt REXt GDPPCt - TDlt_1 FDlt_1 DCt_1 REXt-I GDPPCt_1 TDlt_n FDlt_n
+
• . . •+
An DCt_n + Pt REXt_n GDPPCt_n (6. 8)Jl = error tenus for the variables included; Al -
An
= are 5 x 5 matrices ofcoefficients; Ao = 5 x 1 vector of intercepts.
Domestic private investment equation is (5.7) given as (6.9): lpr;,t FDlt DCt REXt GDPPCt - Ao + A - 1 1 pri,t-l FDlt_1 DCt-I REXt_1 GDPPCt_1 lpri,t-n FDlt_n + .... + An DCt_n + Pt REXt_n GDPPCt_n (6.9)
Il = error terms for the variables included; AI -An = are 5 x 5 matrices of
coefficients; Ao = 5 x 1 vector of intercepts.
Domestic public investment equation (5.8) expressed as (6. 1 0):
Ipub,t Ipub,t-I I pub,t-n
FDlt FDlt-l FDlt_n
DCt = Ao + AI DCt-I + .... + An DCt_n + Pt (6. 1 0)
REXt REXt_1 REXt_n
GDPPCt GDPPCt-I GDPPCt_n
Il = error terms for the variables included; AI -An = are 5 x 5 matrices of
coefficients; Ao = 5 x 1 vector of intercepts.
Since none of these equations in the capital formation model includes dummy variables the exogenous component of the VAR system has been deleted.
Labour productivity equation (5.9) is specified as (6. 1 1 ):
LP' FD� HCt Clt Lt OT; - Ao + A - 1 LP,_I FDI�_I HCt_1 Clt_1 Lt_I OT; LP'_n FDI�_n + .... + An HCt_n + Pt CI,_n Lt-n OT;_n (6. 1 1 )
Il = error tenus for the variables included; AI -An = are 6 x 6 matrices of
coefficients; Ao = 6 x 1 vector of intercepts.
In this approach, the selection of lag length is an important issue as it significantly
influences the test results.9 It is better to use certain information criteria for selecting the appropriate lag length to avoid the risk of arbitrariness. The popular criteria suggested in the literature are the Akaike information criteria (AIC), and Schwartz Bayesian Criteria (SBC). This study employs both to obtain reliable lag structures for the proposed models. In addition, the choice of the lag length is tested on a host of diagnostic tests related to the properties of the residuals.
After selecting the appropriate lag length, the approach suggested in 10hansen ( 1 988, 1 992) and 10hansen and luselius ( 1 990) will be employed to determine the number of cointegaration vectors. As mentioned before, lohansen ( 1 988) and 10hansen and luselius ( 1 990) proposed the use of both the maximum eigenvalue and the trace statistics to test the number of cointergarting vectors. Consequently the null hypothesis
IS:
Hr: Rank (IT) = r (6. 1 2)
Against
Hr+l : RarIk (IT) = r + 1 ; r = 1 , 2, . . . . , M -1 , in equation (6. 1 2)
The log-likelihood ratio statistics for the maximum eigenvalue is given as:
where Ar is the rth largest eigenvalue.
Alternatively, in the trace test the n ull hypothesis H(r) defmed by (6. 1 2) against the trend-stationarity is given by:
9 lung and Marshall ( 1 985) pointed out that the determination of appropriate lag length is problematic, especially when there are many variables to be examined and when few observations are taken.
LR(H/Hm) = -tU: log ( l - I..r+d (6. l 3)
where, for r = 1 , 2 .. . .. , m-I and Ar+l, . Ar+l, . . . . Am are the largest eigenvalues.
If the variables are non-stationary, say 1( 1 ), it may be helpful to take the first difference of the variables to make them 1(0) and then use the differenced variables in the V AR system. However, if the 1( 1 ) variables are cointegrated, differencing the variables will lead to the loss of important and useful information about the long-run relationships. That is, omitting the cointegrating combination is a specification error in a V AR system and such VAR models provide no information about the long-run which is of considerable interest to economists (Patterson, 2000).
Therefore, based on the procedures enunciated by lohansen ( 1 988) and lohansen and
luselius ( 1 990) the VAR equations ((6.3), (6.4), (6.5), (6.6), (6.7), (6.8), (6.9), (6. 1 0) and
(6. 1 1 )) of the respective models developed in this Chapter will be tested, and if
cointegration exists then the VECM will be applied to investigate the interrelationships.
This co integrating model of V AR is a restricted version of the traditional VAR10 and, as
with bi-variate cointegration, an error correction component is required in a V AR
containing co integrated variables.
Thus, Equation (6.2) can now be transformed into a VECM form as follows:
p-I
/)J" = ao + all
+ IT Z,_I
+ L [;/)J,t-j+ 'I' w, + J.1,
(6. 1 4);=1
where
• Zt = is an (m x l) vector of jointly determined endogenous 1(1) variables;
• Wt is a (q x 1 ) vector of exogenous/deterministic 1(0) variables excluding the
intercepts and/or trends;
• ).Lt is the error terms.
1 0
The IT matrix conveys information about the long-run relationship between Yt variables (key macroeconomic variables proposed in this study). The rank of IT is the number of linearly independent and stationary linear combinations of the macroeconomic variables. Therefore, testing cointegration involves testing the rank r matrix of IT by examining whether the eigenvalues of IT are significantly different from zero. Three possible conditions exist: (i) The IT matrix has full column rank, implying that the Zt was stationary in levels to begin with; (ii) The IT matrix has zero rank, which implies the system is an unrestricted VAR; and finally, (iii) The n matrix has rank r such as 0 < r > n, indicating that there exist r linear combinations of Yt that are cointegrated. If condition (iii) prevails, then IT can be decomposed into a and � , such that IT = a� ' .
The vectors of � represent the r linear cointegrating relationships, and by testing the significance of the � coefficients it can be known whether the variables enter the cointegrating relationship significantly. The loading matrix a represents the error correction parameters, which can be interpreted as speed of adjustment parameters. As 10hansen ( 1 992) demonstrated, the significance of the a coefficients provides information about weak exogeneity of the variables in the system. An insignificant coefficient of ag suggests the variable g is weakly exogenous - it drives the co movements of the variables in the co integrated system, while a significant a indicates the variable endogenously reacts to the past errors and adjusts to restore the long-run relationship.
Given the results of the 10hansen ( 1 988) and lohansen and luselius ( 1 990) procedure and following the Granger Representation Theorem 1 1 each equation in the aforementioned V AR system w ill b e t ransformed i nto V ECM e quations by adding an error correction term (EeT). 12 It would be, therefore, possible to separate the long-run relationship between economic variables from their shot-run responses, and to determine the direction of Granger causality.
1 1 According to t he Granger Representation Theorem, with cointegrated I ( I ) series, an ECT has to b e included i n t he first differenced model in order to capture the equilibrium relationships among the cointegrated variables in their dynamic behaviour.
12 As the results are discussed in Chapter Seven, the corresponding VECM models of the V AR equations, (6.3) to (6. 1 1), are given in Appendix 7.3.
6.5. 1 Causality Test
This empirical work then extended to the issue of Granger-causality between FDI and major key macroeconomic variables, where very little attention has been given in the empirical literatureY Granger ( 1 986, 1 988) and Bngle and Granger ( 1 987) provide a test of c ausality t hat t akes i nto a ccount the i nformation p rovided b y t he c ointegrated properties of variables. Following Granger ( 1 969), an economic time-series YI is said to be 'Granger-caused' by another series Xt if the information in the past and present values of Xt helps to improve the forecasts of the Yt variable. Granger-causality tests in a strictly bi-variate framework is computationally easier, but the omission of other relevant variables could result in spurious causality (Granger, 1 969). Caporale et al. ( 1 998) showed that the omission of an important variable results in invalid inferences about the causality structure of the system unless causality is in the direction of the omitted variable(s), but not vice versa. The procedure for testing Granger-causality becomes more complex when the variables Xt and YI have unit roots. In such cases it is useful to re-parameterise the m odel in a n equivalent VECM (see Bngle and Granger,
1 987; Johansen, 1 988).
This study tries to fmd the causality between FDI and the suggested key macroeconomic variables, it, therefore, assumed that there are only two variables included in the models in a VECM procedure. This requires a re-parameterisation of the models to test the causality between FDI and maj or macroeconomic variables.
13 For example Kasibhatla and Sawhney ( 1 996), cited in Axarlaglou et al. (2002), tested the causality between FDI and GDP growth for US data for the period 1 970- 1 990, and found growth Granger-cause FDI not the reverse. Chakraborty and Basu (2002) found similar evidence in the study of India. Nevertheless, Zhang ( 1 999) found FDI to enhance economic growth in the short-run and the long-run. in the case of some selected East Asian and Latin American countries. Conflicting evidence in terms of causality could be found in the studies of Khan and Leng ( 1 997), while studies on the FDI trade nexus consider mainly outward FDI and exports (see, Alguacil and Orts (2002), with the exception of the study of Liu et al. (2001 ). As Kumar ( 1 996) concluded the conflicting results of the studies are perhaps evidence of the difficulty of disentangling FDI's effect on growth from the effects on growth of FDI determinants. Further, the conflicting and limited evidence from growth-FDI nexus and FDI trade nexus needs to be shown empirically and unequivocally to prove with individual country experiences. Thus, based on these arguments the current study extends the previous literature in that direction.
The re-parameterising of the equation can be shown in the following fonn14:
p-I p-I
�J; = 1/
+
i=1 I ai�J;-i +j=1
LPjM'_i +
BECT,_I + P,p-I p-I
M,
= 1/'+
i=1 I ri�J;-i +j=1
L8jMI-J +
<DECT,_I+
P;(6. 1 5)
(6. 1 6)
where the lagged EeT are the lagged residuals from the cointegrating relation between
Y and X. However, there are now two sources of the causation of Yt by Xt. either through the lagged dynamic tenn �Xt-}' if all the �i are not equal to zero, or through the lagged EeT, if e is nonzero, Similarly, Xt is Granger-caused by Yt either through the lagged dynamic terms /:). Yt-I , if all the 'Yi are not equal to zero, or through the lagged EeT, if <l> is nonzero. Based on this concept, this study uses Granger-causality tests to examine possible causal relationships between FDI and GDP growth, exports and domestic investment. Granger (1 988) suggests that if a co integrating vector exists among the variables, there is causality among these variables in at least one direction. The Granger-causality tests can thus be used to investigate the nature of the relationship. The variables are 1( 1 ) and co integrated: employing the equation (6. 1 5) and (6. 1 6) as a base, Granger-causality will be tested for the VAR models specified in section 6.5. Granger-causality tests are examined by the Wald test and/or the t-test of the of the EeT.
6.5.2 Impulse Response and Variance Decomposition
Since the estimated coefficients of VAR are difficult to interpret, it is necessary to look
at the impulse response functions (IRF) and forecast error variance decompositions
(FEV) of a system to draw conclusions about a VAR. These two functions together are
called innovation accounting, which is used in this study to analyse the impact of unanticipated shocks and to examine the relationships between economic variables. According to Pesaran and Pesaran (1 997), "IRF measures the time profile of the effect
14 See Oxley and Greasley { I 998); Mills ( l 998); Chang et al. (2001 ).
of shocks on the future states of a dynamical system" (p. 423). That is, it is possible to determine the reaction of the variables in the VAR to a one standard deviation shock in a
given variable. Two types of IRFs have been developed, one by Sims ( 1 980) orthogonalised IRFs, and the other by Koop, Pesaran and Potter (1 996), IS which is the generalised IRF.
These two can be distinguished by the relative importance they place on the ordering of the variables in the VAR. It should be noted that the orthogonalised approach is problematic when the researcher has limited knowledge of the order of the variables. However, generalised IRFs are independent of the order of the variables in the V AR.
The impulse responses will be similar for the first variable in the VAR or in situations where the system covariance matrix of error is a diagonal matrix.
Lutkepohl and Reimers ( 1 992) have developed IRF analysis of the co integrated VAR.
They drew o n the full information maximum likelihood-based procedure developed by 10hansen and luselius ( 1 990). This VAR model is very powerful and flexible because it can accommodate stationary, difference operators, and cointegrated V AR systems. Lutkepohl and Reimers ( 1 992) stated that it might be deceptive to interpret the coefficient from the co integrating relationships as the long-run elasticities or semi elasticities of the corresponding variables. They suggested IRF analysis of the co integrated system with multiple co integrating roots to be more appropriate. The IRFs of cointegrating V AR can be computed in the same way as in the case of stationary V AR
models. Pesaran and Pesaran ( 1 997) noted that the main difference is the "matrices Ai, in the moving average representation of the Zt process tend to zero when the underlying
V AR model is trend-stationary and the tend to non-zero rank deficient matrix C( 1 ),